It's happened to me, and it basically just doesn't work without pressing really hard. Unlike the other button, L, which clicks then pops out after, it is like there is something stuck underneath. I sent it to Gamestation where I got it, they took it off me for a day, then said they could send it to Nintendo for me. So they did, and 4 weeks later I got it back, with a new stylus (chewed a little), and new L and R buttons. The model has been cleaned very well too.
It's clearly fixable, just ask the people where you got it from.
- James